Infinite Problem Generator: Verifiably Scaling Physics Reasoning Data with Agentic Workflows

• URL: http://arxiv.org/abs/2603.14486v1
• Date: Sun, 15 Mar 2026 17:08:50 GMT
• Title: Infinite Problem Generator: Verifiably Scaling Physics Reasoning Data with Agentic Workflows
• Abstract summary: We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability.<n>IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency.<n>We release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds.
• Score: 1.3986052226424095
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the reasoning traces required for fine-tuning. We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability through a Formula-as-Code paradigm. Unlike probabilistic text generation, IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency. As a proof-of-concept, we release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds. The corpus demonstrates high structural diversity, spanning 102 unique physical formulas with an average complexity of 3.05 formulas per problem. Furthermore, we identify a Complexity Blueprint, demonstrating a strong linear correlation ($R^2 \approx 0.95$) between formula count and verification code length. This relationship establishes code complexity as a precise, proxy-free metric for problem difficulty, enabling controllable curriculum generation. We release the full IPG pipeline, the ClassicalMechanicsV1 dataset, and our evaluation report to support reproducible research in reasoning-intensive domains.

Related papers

• What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code [72.9921566968371]
  We revisit the claim that code improves reasoning through controlled pretraining experiments on a 10T-token corpus with fine-grained domain separation.<n>Code substantially improves programming ability but does not act as a general reasoning enhancer.<n>Cross-domain structured reasoning traces, such as code-text and math-text mixtures, are better explained.
  arXiv  Detail & Related papers  (2026-05-19T12:37:01Z)
• MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis [26.328617109421327]
  This paper proposes a hierarchical framework that formulates data synthesis as an unsupervised optimization problem.<n>We introduce a Legislator-Executor paradigm: The Legislator adversarially evolves structured generation blueprints encoding the constraints of the problem, while the Executor instantiates these specifications into diverse natural language scenarios.<n> Experiments conducted on a total of 10 models across the Qwen, Llama, Mistral, and Gemma series demonstrate that our method achieves notable results.
  arXiv  Detail & Related papers  (2026-04-13T08:48:12Z)
• SymPyBench: A Dynamic Benchmark for Scientific Reasoning with Executable Python Code [7.0748516420242495]
  We introduce, a large-scale synthetic benchmark of 15,045 university-level physics problems (90/10% train/test split)<n>Each problem is fully parameterized, supporting an effectively infinite range of input configurations.<n>The benchmark contains three question types: MC-Symbolic (multiple-choice with symbolic options), MC-Numerical (multiple-choice with numerical options), and free-form (open-ended responses)
  arXiv  Detail & Related papers  (2025-12-05T18:50:48Z)
• Chain of Unit-Physics: A Primitive-Centric Approach to Scientific Code Synthesis [0.0]
  This work conceptualizes an inverse approach to code design: a first-principles (or primitives)-centric, multi-agent system in which human expert knowledge is encoded as unit-physics tests that explicitly constrain code generation.<n>As datasets and models evolve, zero-shot code accuracy will improve; however, the Chain of Unit-Physics framework goes further by embedding first-principles analysis that is foundational to scientific codes.
  arXiv  Detail & Related papers  (2025-11-30T18:16:50Z)
• Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis for Large Reasoning Models [54.29243291958429]
  We develop a problem generator that reasons explicitly to plan problem directions before synthesis.<n>We treat the solver's feedback on synthetic problems as a reward signal, enabling the generator to calibrate difficulty.<n>Our method achieves an average improvement of 2.5% and generalizes to both language and vision-language models.
  arXiv  Detail & Related papers  (2025-11-13T03:08:51Z)
• Lean Meets Theoretical Computer Science: Scalable Synthesis of Theorem Proving Challenges in Formal-Informal Pairs [41.29431283264807]
  We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems.<n>We demonstrate this approach on two TCS domains: Busy Beaver problems, which involve proving bounds on Turing machine halting behavior, and Mixed Boolean Arithmetic problems, which combine logical and arithmetic reasoning.<n>Our framework automatically synthesizes problems with parallel formal (Lean4) and informal (Markdown) specifications, creating a scalable pipeline for generating verified proof challenges.
  arXiv  Detail & Related papers  (2025-08-21T14:15:40Z)
• FormulaOne: Measuring the Depth of Algorithmic Reasoning Beyond Competitive Programming [19.576944188747166]
  FormulaOne is a benchmark for graph theory, logic, and algorithms.<n>Our problems are incredibly demanding, requiring an array of reasoning steps.<n>Remarkably, state-of-the-art models like OpenAI's o3 fail entirely on FormulaOne.
  arXiv  Detail & Related papers  (2025-07-17T17:53:55Z)
• RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library [58.404895570822184]
  RV-Syn is a novel mathematical Synthesis approach.<n>It generates graphs as solutions by combining Python-formatted functions from this library.<n>Based on the constructed graph, we achieve solution-guided logic-aware problem generation.
  arXiv  Detail & Related papers  (2025-04-29T04:42:02Z)
• DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning [95.31714779585272]
  DeepMath-103K is a large-scale mathematical dataset designed with high difficulty (primarily levels 5-9)<n>It includes rigorous decontamination against numerous benchmarks, and verifiable answers for rule-based RL reward.<n>DeepMath-103K fosters the development of generalizable and advancing reasoning.
  arXiv  Detail & Related papers  (2025-04-15T17:59:51Z)
• PromptCoT: Synthesizing Olympiad-level Problems for Mathematical Reasoning in Large Language Models [59.920971312822736]
  We introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems.<n>The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction.<n>Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods.
  arXiv  Detail & Related papers  (2025-03-04T06:32:30Z)
• MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs [80.96119560172224]
  MathGAP generates problem statements and chain-of-thought reasoning traces according to specifications about their arithmetic proof structure.<n>Using MathGAP, we find that LLMs show a significant decrease in performance as proofs get deeper and wider.
  arXiv  Detail & Related papers  (2024-10-17T12:48:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.